When I was a student, a composition was usually an assignment or the last part of the many examination papers that demands me to write for a given topic with specific requirements. But I also experienced and enjoyed writing for my own purposes: to express my feelings, to communicate with others, or to entertain my audience. So I would love to define composition as writing we do to express ourselves (our ideas and feelings) and communicate with the others in ways of describing, narrating, explaining, elaborating, arguing, etc. We start with a central idea in mind and use various genres, languages and rhetoric skills to present it to the audience (the audience sometimes can be the readers themselves) and impress the audience.